Seasonal Effects on a Beddington-DeAngelis Type Predator-Prey System with Impulsive Perturbations

Seasonal Effects on a Beddington-DeAngelis Type Predator-Prey System with Impulsive Perturbations

We study a Beddington-DeAngelis type predator-prey system with impulsive perturbation and seasonal effects. First, we numerically observe the influence of seasonal effects on the system without impulsive perturbations. Next, we find the conditions for the local and global stabilities of prey-free pe...

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Main Authors: Hunki Baek, Younghae Do
Format: Article
Language:English
Published: Hindawi Limited 2009-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2009/695121
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spelling doaj-68729815cb35481a8916617e6ae8b0392020-11-24T22:26:53ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092009-01-01200910.1155/2009/695121695121Seasonal Effects on a Beddington-DeAngelis Type Predator-Prey System with Impulsive PerturbationsHunki Baek0Younghae Do1Department of Mathematics, Kyungpook National University, Daegu 702-701, South KoreaDepartment of Mathematics, Kyungpook National University, Daegu 702-701, South KoreaWe study a Beddington-DeAngelis type predator-prey system with impulsive perturbation and seasonal effects. First, we numerically observe the influence of seasonal effects on the system without impulsive perturbations. Next, we find the conditions for the local and global stabilities of prey-free periodic solutions by using Floquet theory for the impulsive equation and small amplitude perturbation skills, and for the permanence of the system via comparison theorem. Finally, we show that seasonal effects and impulsive perturbation can give birth to various kinds of dynamical behavior of the system including chaotic phenomena by numerical simulations.http://dx.doi.org/10.1155/2009/695121
collection DOAJ
language English
format Article
sources DOAJ
author Hunki Baek
Younghae Do
spellingShingle Hunki Baek
Younghae Do
Seasonal Effects on a Beddington-DeAngelis Type Predator-Prey System with Impulsive Perturbations
Abstract and Applied Analysis
author_facet Hunki Baek
Younghae Do
author_sort Hunki Baek
title Seasonal Effects on a Beddington-DeAngelis Type Predator-Prey System with Impulsive Perturbations
title_short Seasonal Effects on a Beddington-DeAngelis Type Predator-Prey System with Impulsive Perturbations
title_full Seasonal Effects on a Beddington-DeAngelis Type Predator-Prey System with Impulsive Perturbations
title_fullStr Seasonal Effects on a Beddington-DeAngelis Type Predator-Prey System with Impulsive Perturbations
title_full_unstemmed Seasonal Effects on a Beddington-DeAngelis Type Predator-Prey System with Impulsive Perturbations
title_sort seasonal effects on a beddington-deangelis type predator-prey system with impulsive perturbations
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2009-01-01
description We study a Beddington-DeAngelis type predator-prey system with impulsive perturbation and seasonal effects. First, we numerically observe the influence of seasonal effects on the system without impulsive perturbations. Next, we find the conditions for the local and global stabilities of prey-free periodic solutions by using Floquet theory for the impulsive equation and small amplitude perturbation skills, and for the permanence of the system via comparison theorem. Finally, we show that seasonal effects and impulsive perturbation can give birth to various kinds of dynamical behavior of the system including chaotic phenomena by numerical simulations.
url http://dx.doi.org/10.1155/2009/695121
work_keys_str_mv AT hunkibaek seasonaleffectsonabeddingtondeangelistypepredatorpreysystemwithimpulsiveperturbations
AT younghaedo seasonaleffectsonabeddingtondeangelistypepredatorpreysystemwithimpulsiveperturbations
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